Least Common Multiple (LCM) of 33 and 144
The least common multiple (LCM) of 33 and 144 is 1584.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 33 and 144?
First, calculate the GCD of 33 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 144 = 0 remainder 33 |
| 2 | 144 ÷ 33 = 4 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 168 | 18984 |
| 181 and 155 | 28055 |
| 79 and 36 | 2844 |
| 101 and 101 | 101 |
| 72 and 187 | 13464 |